Matlab: draw the Pole-Zero plot of the Z-transform

To plot the Pole-Zero diagram of the Z-transform on the Z-plane, write the transfer function in the form of b(z)/a(z) in terms of z^-n:

z(z-1)/(z+1/2)(z-1/4) = (1 - z^-1)/(1+1/2z^-1)(1-1/4 z^-1) =  (1 - z^-1)/(1+1/4 z^-1-1/8 z^-2)

Call the zplane() function to draw the ploe-zero plot with coefficients of b(z)/a(z):

>> b=[1,-1];
>> a=[1,1/4,-1/8];
>> zplane(b,a);

Result:

The zeros are at 0 and 1 and the poles are at -1/2 and 1/4.

Reference:

zplane (MathWorks)